Question

A semi-annual corporate bond has a coupon rate of 9 percent per year. The face value. is $1,000. The market interest rate (yield to maturity) for this bond today is 10.5 percent. This bond has 25 years. before maturity. What is the price of this bond today? (5 points). b. What is the current yield for this bond? (3 points) c. Why is the current yield different from the current market rate of this bond? (2 points)

Answer 1

a. Semi-annual bond

annual coupon rate = 9%, semi-annual coupon rate = 9%/2 = 4.5%

Face value = FV = 1000

Coupon paid semi-annualy = C = 4.5%*1000 = 45

The bond has 25 years before maturity

Total number of periods till maturity = 25*2 = i = 50

annual YTM = 10.5%

semi-annual YTM = 10.5%/2

Price of the bond can be calculated using the below formula:

using a scientific calcculator:

PV = 790.7764992110+77.42741759 = 868.2039167982

Therefore, price of the bond today = 868.2039167982

b. Current yield can be calculated using the below formula:

Semi-annual bond yield = C/PV = 45/868.2039167982 = 5.18311414281047%

Annual current yield = (1+5.18311414281047%)²-1 = 10.634875%

Current yield = 10.634875%

c. The current yield of the bond differs from the current market rate be as the bond is trading at discount and its price is less than its face value. If the bond were trading at par then its current yield would have been similar to its current market rate.